Though Mr. Rawlins left the party, many newcomers are staying, and whether the Conservatives remain a broad church or become a club for dedicated supporters of Brexit will in part shape the future of British politics.

“The Conservative Party, famed for 150-plus years for its pragmatism, has effectively become an ideological party, or at least its members have,” said Tony Travers, a professor of government at the London School of Economics. “Even if you do have a reasonable filter, you can’t stop a party being shifted quickly in one direction or another by individuals whose views are significantly to one side of its median policy position.”

As it stands, almost anyone willing to pay the 25 pound annual membership fee — about $30 — can join, and while local party officials do cursory internet searches on applicants’ names, they do not tend to bar people merely for dabbling in rival parties.

That can create difficult questions for a political system dominated by two parties, in which joining either the Conservatives or the opposition Labour Party can give voters vastly disproportionate power.

New Members Flood U.K.’s Conservatives, Yanking the Party Right – The New York Times